No. Since these addresses refer to different output types, they are not interchangeable.
Addresses are shorthand to describe output scripts. Addresses starting with 1… describe Pay to Public Key Hash (P2PKH) outputs, while bech32(m) addresses starting with bc1… describe native segwit outputs (Pay to Witness Public Key Hash (P2WPKH), Pay to Witness Script Hash (P2WSH), and Pay to Taproot (P2TR)). While they all use private keys from the secp256k1 elliptic curve as the underlying secret, they use the keys differently in their locking mechanisms.
Wallets backed up before a transaction took place will never know about that transaction, but they will be able to discover any relevant transactions when they get reconnected to the network and hear about new blocks. Generally, wallets store private keys, and it is possible to derive all output scripts corresponding to the different types from these keys.
Generally, you should not need to worry about how a native segwit address and legacy address are related. Today, almost everyone should be able to send to native segwit addresses. If the sender that's trying to pay you cannot send to bech32 addresses, you should be able to generate a legacy addresses from Bitcoin Core either via the command line or the GUI.
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